I do have a personal interest in the subject, seeing as I have two half-Asian sons.
I think the biggest problem I see is probably perception of Asian men as not masculine/not good looking. To me, this is the worst problem at a statistical level. Compared to that, snickering about being bad drivers is like saying that white people can't dance ... it's not a big deal, you will look lame complaining about it (why? because in the overall context of a bundle of stereotypes for each group, it's not a big deal). Hate crimes against Asians do happen, as do anti-Semitic hate crimes ... a terrible thing, sure, but statistically I would think Asians are less likely to be criminal victims than other races.
The real problem that I see (or at least am concerned about wrt my own sons) is that Asian men are stereotyped negatively when it comes to physical attractiveness/masculinity, which indeed sucks. Part of this is because recent immigrants aren't fluent in the code of projecting masculinity; the FOB syndrome, although this is declining nowadays. Part is because the number one way that men in America demonstrate masculinity is through sports, being huge and swole and fast and such, and Asians are statistically as underrepresented in pro sports as they are overrepresented at Harvard. But part of it is just aesthetic prejudice; the exact same face is seen as beautiful if female but not if male.
It also doesn't help, to my mind, that modern East Asian culture seems to hyper-emphasize being some sort of androgynous 'prettier than a girl' type of young boy. This kind of thing is rampant in Korea, and with the rise of "grass eating boys" in Japan it's even worse.